2VP_2_INTEGR

#include <iostream>
#include <cmath>
#include <conio.h>
#include <fstream>

using namespace std;


double func (double x){
    return sqrt (2 * x + 1);
}


double Sr_pr (double a,double b,int N){
    double Summ = 0;
    double h = (b - a) / N;

    for (int n = 1; n <= N; n++){
        Summ += func (a + h*(2 * n - 1) / 2)*h;
    }
    return Summ;
}

double trapeze (double a,double b,int N){
    double Summ = 0;
    double h = (b - a) / N;

    for (int n = 1; n <= N; n++){
        Summ += h*(func (a + h*(n - 1)) + func (a + h*n)) / 2;
    }
    return Summ;
}

double Simpson (double a,double b,int N){
    double Summ = 0;
    double h = (b - a) / N;

    for (int n = 1; n <= N; n++){
        Summ += (func (a + h*(n - 1)) + 4 * func (a + h*(2 * n - 1) / 2) + func (a + h*n))*h / 6;
    }
    return Summ;
}

int main (){
    setlocale (LC_ALL,"Russian");

    cout.precision (10);

    cout << "Прямоуг 20 " << Sr_pr (0,1,20) << "\n";
    cout << "Прямоуг 50 " << Sr_pr (0,1,50) << "\n";
    cout << "Прямоуг 100 " << Sr_pr (0,1,100) << "\n\n";

    cout << "Трапеция 20 " << trapeze (0,1,20) << "\n";
    cout << "Трапеция 50 " << trapeze (0,1,50) << "\n";
    cout << "Трапеция 100 " << trapeze (0,1,100) << "\n\n";

    cout << "Симпсон 20 " << Simpson (0,1,20) << "\n";
    cout << "Симпсон 50 " << Simpson (0,1,50) << "\n";
    cout << "Симпсон 100 " << Simpson (0,1,100) << "\n\n";

    system ("pause");
    return 0;
}